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Current Launch vehicles and upper stages must only keep their fuels for minutes or hours, so they are only insulated to keep boiloff to a few % per day - I've seen 21% per day quoted for Centaur on coasts to GEO.

For proposed "fuel depots" or Mars missions, hydrogen (and oxygen) must be kept liquid for years with minimal losses, is this achievable purely with insulation and sun shading or are refrigeration methods being considered?

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NASA had a zero boil-off tank on the ISS for some time, but they haven't updated much of that page unfortunately. With CRS-16 they sent the third in a series of robotic missions to the ISS that is supposed to maintain cryogenic fluid for six months, as well as transfer said cryogenic fluids in microgravity. That mission launched in early December, so we should hear more later this year. Back as far as 2012 TRL of 4-6 for storage of hydrolox had been accomplished (you can find what TRL means here), with a TRL of 6 being a fully functional prototype.

For more generalized proposals, there was one from ULA in 2008, a somewhat similar one from a group not too much later, some tangential details in relation to a single depot being used for multiple missions, and this large 2011 NASA proposal that got almost no mention in the public sphere. In general it seems for long-term storage most proposals are assuming some sort of active cooling over passive protection.

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